In [1]}, Kaufman proved that if \(A \subset \mathbb {R}^2\)  is a Borel set and if \(\pi _e\colon \mathbb {R}^2\rightarrow \mathbb {R}\)  is the orthogonal projection onto \(\operatorname{span}(e)\) , then \(\pi _e(A)\)  can only have small dimension for a small exceptional set of directions \(e \in \mathbb {S}^1\) .
